Photoelastic Gel Microscopy (PGM): towards beacon-free direct imaging of cellular traction forces

Over the last two decades, it has been shown that mechanical forces play a crucial role in determining cellular
processes - both in physiological and pathological conditions - which led to the emerging field of mechanobiology
[1]. It has been demonstrated that cells mechanically interact with their environment in a bidirectional fashion,
where they are able to exert forces and, in like manner, decipher mechanical cues, such as bulk stiffness, spatiotemporal changes in stiffness, stress relaxation, nanotopography or the presence of shear forces [2]. Whereas
the exact molecular pathways governing this bidirectional interplay remain unclear, the mechanical exchange of
forces between the intracellular and extracellular compartments is known to occur via focal adhesions. These
are supramolecular complexes, often of several square micrometres in area, bridging the intracellular and extracellular environments through a multitude of proteins [3]. As a result, cells are able to pull on their surrounding
environment - via forces that are intracellularly generated through the well known mechanism of acto-myosin
contractility - and transduced externally via focal adhesions. Cells then sense the mechanical response of their
surrounding, being endogenous (i.e. the Extracellular Matrix or ECM) or man-made (e.g. hydrogels) via the
same transducing machinery, which, in turn, can give rise and influence a large number of cellular processes [1].
As a consequence, in order to fully exploit the potential of mechanobiology for diagnostic applications, there is
an increasing need for specialised tools providing the ability to reveal and measure forces down to the single
cell level with high accuracy and reproducibility.
In this context, the contractile forces that cells exert on their substrate are of particular interest - resulting
in contractile stresses commonly referred to as traction forces. These forces have been known to strongly
participate in the development and establishment of the three-dimensional organisation of tissues and organs in
physiological conditions [4]. Conversely, looking at the impairment of the physiological pattern of traction forces,
might be a way to infer about the onset of an aberrant pathology, such as a cancer, known to be associated to
a change in the mechanical behaviour of cells, which detach from their original location, extrude, invade and
finally assume a different three dimensional organisation, the metastasis [5, 6].
Whereas the path to disclose the wealth of implications of mechanobiology is still in its infancy, the first
steps have been taken in the context of biomedical research addressing the organisation of traction forces at the
level of the single cell, and evaluating how specific events - either biochemical, genetic or mechanical - in turn
influence this pattern. The most common approach is to measure cellular forces at the cell-matrix interface.
This field has grown rapidly since it first emerged 15 years ago, leading to what is now known as Traction Force
Microscopy (TFM) [7, 8]. The most common TFM approach is to seed cells on a substrate of known stiffness
(a hydrogel) containing reference fluorescent beads. As cells apply tractions on the substrate, the displacement
of such beads is optically monitored and the exerted forces retrieved from the displacement. The indirect
measurement of forces requires both a constitutive model of the substrate's mechanical response and precise
knowledge of its physical properties. This is easily understood with the example of a linear elastic spring, whose
constitutive model is given by Hooke's law (F = k(x - x0)), where F is the force, k is the spring's stiffness
and x - x0 is the spring's displacement with respect to its reference position, x0. Without a measurement of
x (and its reference state x0), knowledge of k and the overall constitutive law, the force, in principle, cannot
be retrieved [7, 8]. Notably, this is not a triv